Model Reference Adaptive Stabilizing Control for Leader-Following Consensus

Complex networks, neuroscience, and other applications have shown examples of multi-agent adaptive systems that must follow (over possibly short times) reference dynamics that are neither Hurwitz nor neutrally stable. However, such leader-following behavior would be impossible with existing adaptive consensus methods, e.g., based on model reference adaptive control (MRAC), since the stability of the reference dynamics is required. To fill this gap, we propose a novel model reference adaptive stabilizing control (MRASC) framework for leader-following consensus of multi-agent systems with unknown and heterogeneous dynamics. Differently from several approaches in the leader-following consensus literature, the proposed framework is free of any extra distributed observer layer for the leader's signal, as the reconstruction of such signals is intrinsic in the adaptive laws. Besides, the framework does not require Hurwitz or neutral stability of the leader and generalizes existing acyclic requirements on the communication graph among the follower. Starting from any weakly connected communication digraph, the proposed method allows to derive a lower bound, useful from the network design point of view, for the minimum number of followers that should be pinned by the leader.